Question

What is the solution to the equation below? Round your answer to two

decimal places.
4* = 9.2
O A. x = 0.62
O B. x= 0.96
O c. x= 2.22
O
D. x = 1.60

Answer 1

The Solution to the equation 4ˣ = 9.2 is the option D ) x = 1.60

Explanation:

Given:

`4^(x)=9.2`

To Find:

x = ?

Solution:

We know Logarithmic identity as

`\log (A)^(B)= B\log A\\`

`4^(x)=9.2` .............Given

Taking Log on both the side we have

`\log 4^(x)=\log 9.2\\\textrm{using the above identity we get}\\\\x\log 4 = \log 9.2\\\\x=(\log 9.2)/(\log 4) \\\\\therefore x =(0.9637)/(0.6020) \\\\\therefore x =1.6008\\\\\therefore x = 1.60`

The Solution to the equation 4ˣ = 9.2 is the option D ) x = 1.60